This invention relates to a method and apparatus for characterizing and qualifying dipole and multipole magnets such as those utilized in superconducting subatomic particle accelerating or colliding apparatus including testing the magnitude, stability and homogeneity of the magnetic field of the magnets.
In superconducting subatomic particle accelerating or colliding apparatus, superconducting magnets are utilized to accelerate, focus or direct subatomic particles through a bore within the magnets and in a linear or curved path. The particles are accelerated over long distances and, in order to control the direction of particle acceleration, it is essential that the magnetic field generated by the magnets be known and well controlled. As presently constructed, the magnets comprise a magnetic flux generator such as a super-conducting coil structure assembled around a magnetically permeable metal bore tube. Correction coils positioned within or outside of the main superconducting coil and the metal bore tube are provided to compensate for magnetic field distortions caused by imperfections of design winding or placement of magnet elements and by saturation of the metal housing for the coils which surrounds the coils. In order to compensate for magnetic field inhomogeneities, the current to the trim coils must be controlled accurately. However, in order to determine the current needed for the trim coils, it is necessary to determine the nature and extent of the field inhomogeneities by mapping the static magnetic field generated by the main coils. While localized measurements at cryogenic temperatures and at high fields are possible using existing technology, characterization of homogeneity over the extended length and within the narrow bore of the magnet poses a significant challenge. At the present time mapping can be conducted with a long rotating coil, a travelling rotating coil, a planar probe array and a planar NMR array. The long rotating coil comprises a precision bobbin with extended windings and has the disadvantage of geometrical distortion of surface area. It is also difficult to control the coil since it requires rotation within the cryogenic environment. The rotating coil also effects geometrical distortion and requires extended translation within the cryogenic environment as well as requires a measurement cycle with respect to the field instability time constituent. It is also sensitive to Eddy currents and promotes temporal field instability. The planar probe arrays are also undesirable since their use require translation, the measurement cycle is long and the necessary hardware is potentially sensitive to Eddy currents under quench conditions.
Clark et al, J. Appl. Phys., 63 (8) pgs. 4185 and 4186, Apr. 15, 1988 discloses a method and apparatus for measuring the multipole moments of large bending magnets. The apparatus utilizes eight small magnetic resonance coils which are excited to effect a free induction delay signal from the nuclear or electron spin of a working substance such as protons in water or helium-3 positioned within the coils. The frequency of the delay signal is then used to calculate the multipole moments of the magnet.
In defining the multipole moments the following coordinate system is used. The Y axis is vertical, and is the direction of the large dipole field B.sub.o that bends the particle trajectories into a horizontal path. The Z axis is horizontal and along the particle trajectory; the X axis is horizontal and perpendicular to it. The circular boundary upon which the field measurements are made is centered at the origin and lies in the X-Y plane. Points on the circle (radius R) are specified by the angle .theta. measured counterclockwise from the Y axis. Since there are no sources of the magnetic field in this region, each cartesian component of the magnetic field B=(B.sub.x, B.sub.y, B.sub.z) satisfies Laplace's equation. Thus, if any component of B is specified on the boundary of a region, (the circle), it is determined throughout the region (inside the circle). The solution of this boundary value problem gives ##EQU1## The coefficients a.sub.n and b.sub.n are the multipole moments that are used for trajectory stability modeling. They are calculated using the Fourier inversion formulas: ##EQU2##
The frequency of the magnetic resonance precession W.sub.L is given by the magnitude of B of the magnetic field, whereas Eqs. (1)-(3) refer only to its y components. Since the field configuration of the magnets involves only very small components B.sub.x and B.sub.y, and a small variation B.sub.o -B.sub.y along the y direction, the relation between B and W.sub.L to first order in a Taylor series: ##EQU3## where W.sub.L (R,.theta.) is the magnetic resonance frequency at R,.theta. on the circle and y is the magnetic ratio of the resonant spin. Examination of Eqs. (2)-(4) shows that from a measurement of W.sub.L at all points of the boundary, the multipole coefficients are determined.
Within the framework of this approximation, only the variation of B along the y direction is measured [see Eq. 4)]. It is, nevertheless, sufficient to obtain the multipole coefficients. It does not, however, determine the orientation of the probe in the dipole field. For that, other means must be used, such as orientation via the null voltage from a Hall effect probe.
Equations, (2)-(4) imply that W.sub.L is known everywhere on the circular boundary. Since it is not practical to measure it at all points, W.sub.L is measured at a discrete number of points. For this case, one then replaces the integrals in Eqs. (2)-(4) with discrete sums. In the case of M samples at the locations R, 2 m/M with m taking integral values between 0 and M-1. The result is: ##EQU4## where (W.sub.L) is the average of W.sub.L over the circular boundary.
In applying Eqs. (5) and (6) it is important to make the number of probe positions M at least twice as large as the largest multipole index n to avoid the biasing that is inherent in discrete Fourier transforms. Also, going from the continuous case [Eqs. (2) and (3)] to the discrete case [Eqs. (5) and (6)] is an approximation, whose seriousness is easily modeled for a given situation.
Accordingly, it would be desirable to provide a means for measuring the magnitude, stability and homogeneity of a magnetic field which overcomes the disadvantages of the prior art particularly that which is less susceptible to distortions, avoids mechanical motion and which is largely insensitive to Eddy currents.